Below is a list of who is responsible for each topic: (All topics are due 2 cycles from date taught in class)
3-1- Conor, Jack
12/11/09
This section pertains to solving systems of equations in which the equations have the same variables. To solve this system of equation, one must find a pair that satisfies all equations. Meaning, that it will balance and create a linear function. The point of intersection is the answer. This can be used in business, or various other statistics. http://www.algebralab.org/img/0c13bc76-eae8-4d0a-b3c9-04a599399aab.gif
3-2- Kody, Lacey
Solving systems of equations, the substitution method is when an equatiion solved for a variable and substituted and used to find the other variable. ex. x=3y+5 & y=-6-x.
x=3(6-x)-5
x=18-3x-5
4x=13
Elimination metehod, this method is used by eliminatig one variable, you do this by adding or subtracting the equations. ex. 4x-3y=10 & -x+y=11.
3-3- Kayla, Sara
5-1- Becca, Crystal
A monomial is single expression like a number or variable. Any number or variable or expression is a monomial as long as they are not separated by an operation sign. Ex: 5b, 4xy^2. Scientific notation is a easier way to write extremely large or small numbers. You cannot have more than one number to the right of the decimal and no more than two to the left. Ex. 1.35*10^7.
5-2- Zach, John S
A polynomial is made up of monomials. Monomials are is a one term figure that may include numbers, exponents and variables. In order to distinguish between monomials and polynomials, you need to decide whether or not the problem has addition or subtraction signs in it. If there is one addition or subtraction sign, it is a binomial. If there are two addition or subtraction signs, it is a trinomial. Example: 2x + 3 is a binomial. 3x+4y-3 is a trinomial. The degrees of a polynomial can be found by adding the exponents of the variables in the monomial or polynomial. Example: 3x^2 y^6 has a degree of a monomial of 8 because two plus six is the same as eight. In order to simplify a polynomial, you must combine like terms by either adding or subtracting. You must combine all like terms possible. You can not combine an x squared with a x. You may however, combine a x term with another x term. For the distributive property, you must multiply each term outside of the parentheses by every term in the parentheses. When you are multiplying and you have like terms, you add the exponents. Next, when you multiply two binomials, you must use a technique known as F.O.I.L. F stands for first, O stands for outside, I stands for inside, and L stands for last. You multiply the first terms, outside terms, inside terms, and last terms and then combine like terms to get your answer. For multiplying polynomials, you do the same thing as you did for the distributive property except you have more than one term that you are now distributing throughout the parentheses. Example: 2x+3(4y+3x-9)
5-3- Malena, Melissa
x-2 / x^2 + 5x + 6 = x + 3 ( Long Division)
-x^2 +2x
- 3x + 6
- 3x + 6
0
5-4- Rachael, Jon T
Factoring Polynomials-
factor polynomials- Whole numbers are factored using prime numbers. For example, 100 = 2 x 2 x 5 x 5. Many polynomials can also be factored. Their factors, however, are other polynomials. Polynomials that can't be factored are called prime. The FOIL method can help you factor a polynomial into the product of two binomials.So when the C term is negative the sign will be negative and positive and if its positive they will both be the same. When two signs are the same the factor will be positive and when they are different the factor will be negative i.e. -2,-3 it will be +6 and -4,+2 will be -8
9-1- Allison, Alisa 9-1 Rational Expressions are a ratio of two polynomials ex: 2x (x-5) = 2x X x-5 = 2x
(x-5)(x^2-1) x^2-1 x-5 x^2-1
9-2- Jack, Kody
LCM of Polynomials - You must first find the common denominator of two or more numbers or polynomials. Factor each number or polynomial.
ADD and Subtract Rational Expressions - You must have common denominators.
Example Monomial denominators -
1. Find equivalents fractions that have the same denominator
2. Simplify numerator and denominator
3. and add the numerators.
5-7- Conor, Lacey
Rational Exponents
In this sectoin one may learn various methods of solving roots of an equation. This is explained through fractional exponets and root equations with an exponet.
5-8- Kayla, Sara
This chapter deals with radical equations and inequalities.Radical Equations can be solved as follows:
In order to solve a radical equation you must raise each side of the equation to a power that is equal to the radical so that you may eliminate the radical. Here's what I mean;
Because x-1 is under a radical sign it's the same as raising it to the one-half power. In order to reverse that you have to raise it by the second power. After that you have to find the squares. For example, if you have 2² it would become 4, becuase 2 times 2 is four. Then you would solve.
RADICAL INEQUALITIES!-------Radical Inequalities are similar to radical equations. A radcal inequality is a inequality that has a variable in a radicand. You can solve these problems by first, solving the problem in the radicand. The radicand of a square root must be greater than or equal to zero. Next, isolate the radical and elimanate it. then add or subtract the other number(on the same side as the greater than less than sign) to both sides. Then divide both sides by the number next to the variable to get x. Your answer can be tested by using test points and solving and graphing or by useing a chart.
Below is a list of who is responsible for each topic:
(All topics are due 2 cycles from date taught in class)
3-1- Conor, Jack
12/11/09
This section pertains to solving systems of equations in which the equations have the same variables. To solve this system of equation, one must find a pair that satisfies all equations. Meaning, that it will balance and create a linear function. The point of intersection is the answer. This can be used in business, or various other statistics. http://www.algebralab.org/img/0c13bc76-eae8-4d0a-b3c9-04a599399aab.gif
3-2- Kody, Lacey
Solving systems of equations, the substitution method is when an equatiion solved for a variable and substituted and used to find the other variable. ex. x=3y+5 & y=-6-x.
x=3(6-x)-5
x=18-3x-5
4x=13
Elimination metehod, this method is used by eliminatig one variable, you do this by adding or subtracting the equations. ex. 4x-3y=10 & -x+y=11.
3-3- Kayla, Sara
5-1- Becca, Crystal
A monomial is single expression like a number or variable. Any number or variable or expression is a monomial as long as they are not separated by an operation sign. Ex: 5b, 4xy^2. Scientific notation is a easier way to write extremely large or small numbers. You cannot have more than one number to the right of the decimal and no more than two to the left. Ex. 1.35*10^7.
5-2- Zach, John S
A polynomial is made up of monomials. Monomials are is a one term figure that may include numbers, exponents and variables. In order to distinguish between monomials and polynomials, you need to decide whether or not the problem has addition or subtraction signs in it. If there is one addition or subtraction sign, it is a binomial. If there are two addition or subtraction signs, it is a trinomial. Example: 2x + 3 is a binomial. 3x+4y-3 is a trinomial. The degrees of a polynomial can be found by adding the exponents of the variables in the monomial or polynomial. Example: 3x^2 y^6 has a degree of a monomial of 8 because two plus six is the same as eight. In order to simplify a polynomial, you must combine like terms by either adding or subtracting. You must combine all like terms possible. You can not combine an x squared with a x. You may however, combine a x term with another x term. For the distributive property, you must multiply each term outside of the parentheses by every term in the parentheses. When you are multiplying and you have like terms, you add the exponents. Next, when you multiply two binomials, you must use a technique known as F.O.I.L. F stands for first, O stands for outside, I stands for inside, and L stands for last. You multiply the first terms, outside terms, inside terms, and last terms and then combine like terms to get your answer. For multiplying polynomials, you do the same thing as you did for the distributive property except you have more than one term that you are now distributing throughout the parentheses. Example: 2x+3(4y+3x-9)
5-3- Malena, Melissa
x-2 / x^2 + 5x + 6 = x + 3 ( Long Division)
-x^2 +2x
- 3x + 6
- 3x + 6
0
x-2 / x^2 + 5x + 6
1 5 6
-2 -6
1x 3 (Synthetic Division)
5-4- Rachael, Jon T
Factoring Polynomials-
factor polynomials- Whole numbers are factored using prime numbers. For example, 100 = 2 x 2 x 5 x 5. Many polynomials can also be factored. Their factors, however, are other polynomials. Polynomials that can't be factored are called prime. The FOIL method can help you factor a polynomial into the product of two binomials.So when the C term is negative the sign will be negative and positive and if its positive they will both be the same. When two signs are the same the factor will be positive and when they are different the factor will be negative i.e. -2,-3 it will be +6 and -4,+2 will be -8
9-1- Allison, Alisa
9-1 Rational Expressions are a ratio of two polynomials ex: 2x (x-5) = 2x X x-5 = 2x
(x-5)(x^2-1) x^2-1 x-5 x^2-1
9-2- Jack, Kody
LCM of Polynomials - You must first find the common denominator of two or more numbers or polynomials. Factor each number or polynomial.
ADD and Subtract Rational Expressions - You must have common denominators.
Example Monomial denominators -
1. Find equivalents fractions that have the same denominator
2. Simplify numerator and denominator
3. and add the numerators.
5-7- Conor, Lacey
Rational Exponents
In this sectoin one may learn various methods of solving roots of an equation. This is explained through fractional exponets and root equations with an exponet.
5-8- Kayla, Sara
This chapter deals with radical equations and inequalities.Radical Equations can be solved as follows:
In order to solve a radical equation you must raise each side of the equation to a power that is equal to the radical so that you may eliminate the radical. Here's what I mean;
Because x-1 is under a radical sign it's the same as raising it to the one-half power. In order to reverse that you have to raise it by the second power. After that you have to find the squares. For example, if you have 2² it would become 4, becuase 2 times 2 is four. Then you would solve.
RADICAL INEQUALITIES!-------Radical Inequalities are similar to radical equations. A radcal inequality is a inequality that has a variable in a radicand. You can solve these problems by first, solving the problem in the radicand. The radicand of a square root must be greater than or equal to zero. Next, isolate the radical and elimanate it. then add or subtract the other number(on the same side as the greater than less than sign) to both sides. Then divide both sides by the number next to the variable to get x. Your answer can be tested by using test points and solving and graphing or by useing a chart.
5-9- Becca, Crystal